---
tag: HJVM390354
kind: concept
name: Hidden Markov model
msc: [62M05, 60J10]
sources:
  - url: https://en.wikipedia.org/wiki/Hidden_Markov_model
same_as:
  wikidata: Q176769
  wikipedia: Hidden Markov model
---

## Summary

A hidden Markov model is a pair of processes: a [[Markov chain|0G48PYM96Q]] of hidden states and a sequence of observations.
Each observation depends only on the hidden state at the same time.
Only the observations are seen, and the task is to infer the hidden states or the parameters of the model.
Hidden Markov models are used in speech recognition, bioinformatics and signal processing, with efficient algorithms such as the forward algorithm and the Viterbi algorithm.

## Explanations

### L1 human

Think of a casino that secretly switches between a fair die and a loaded die from time to time.
The switching follows a Markov chain, but one sees only the numbers that come up.
From a long run of sixes, one can guess that the loaded die is probably in use.
A hidden Markov model is the precise version of this situation: hidden states that evolve at random, and noisy clues about them.